Online Balanced Repartitioning

Distributed cloud applications, including batch processing, streaming, and scale-out databases, generate a significant amount of network traffic and a considerable fraction of their runtime is due to network activity. This paper initiates the study of deterministic algorithms for collocating frequently communicating nodes in a distributed networked systems in an online fashion. In particular, we introduce the Balanced RePartitioning (BRP) problem: Given an arbitrary sequence of pairwise communication requests between n nodes, with patterns that may change over time, the objective is to dynamically partition the nodes into \(\ell \) clusters, each of size k, at a minimum cost. Every communication request needs to be served: if the communicating nodes are located in the same cluster, the request is served locally, at cost 0; if the nodes are located in different clusters, the request is served remotely using inter-cluster communication, at cost 1. The partitioning can be updated dynamically (i.e., repartitioned), by migrating nodes between clusters at cost \(\alpha \) per node migration. The goal is to devise online algorithms which find a good trade-off between the communication and the migration cost, i.e., “rent” or “buy”, while maintaining partitions which minimize the number of inter-cluster communications. BRP features interesting connections to other well-known online problems. In particular, we show that scenarios with \(\ell =2\) generalize online paging, and scenarios with \(k=2\) constitute a novel online version of maximum matching. We consider settings both with and without cluster-size augmentation. Somewhat surprisingly (and unlike online paging), we prove that any deterministic online algorithm has a competitive ratio of at least k, even with augmentation. Our main technical contribution is an \(O(k \log {k})\)-competitive deterministic algorithm for the setting with (constant) augmentation. This is attractive as, in contrast to \(\ell \), k is likely to be small in practice. For the case of matching (\(k=2\)), we present a constant competitive algorithm that does not rely on augmentation.